Date: 16 SEP 1980 0946-EDT From: DCP at MIT-MC (David C. Plummer) Subject: number of reachable states To: KATZ at USC-ISIF CC: CUBE-HACKERS at MIT-MC Date: 15 Sep 1980 1842-PDT From: Alan R. Katz I have seen the number 4.3 * 10^19 for the number of reachable states for the cube, can anyone tell me how you calculate it? This may have been answered before in this list, but I couldn't find it. Also, someone mentioned that one can make a checkerboard pattern from the Pons Asinorum by trebly rotating the centers by a simple transformation. Can anyone tell me this transformation? (again I may have missed reading it) Reply to either me or the list. Alan ------- Consider the corners. There are 8 of them, and they can go anyplace. This leads to 8 factorial permutations. Each corner can take on three orientations, so this is another factor of 3^8. But the corners have three possible states (trarity [three way parity]) so divide by 3. Now do the same with the edges. 12 edges gives 12 factorial arrangements, times 2^12 oreintations. But the edges have two parities involved, so divide by four (thus giving rise to the 12 states of the cube, one of which has the solved configuration as a member). So if you evaluate 8 12 8!*3 *12!*2 ----------- 3*4 you will get 4.3 * 10^19.